arXiv201412_JP.dvi
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1 J ( 2 ) a a J %, 35%, 3%( 3.4) µ±1.2σ 16 (18 ) J ( ) [1] J [2] [3] a konaka@meijo-u.ac.jp
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2 J [4] * J ( ) 4 NFL MLB NBA NHL [7] (NPB) 2007 ( ) ( ) J J *2 ( ) 2 *1 [5][6] *2 2
3 J 2015 J [1] W1 W2 ( ) Y1 Y3 W1 Y3 W2 Y Y1 Y1 W1, W2, Y2, Y3 W1 W2 Y J Y4-3
4 1 The postseason tournament of J1 League from 2015 season 1 Overlap cases case # overlap(s) teams 1 null 5 2 (Y3, W1) 4 3 (Y2, W1) 4 4 (Y2, W1), (Y3, W2) 3 5 (Y1, W1) 4 6 (Y1, W1), (Y3, W2) 3 7 (Y1, W1), (Y2, W2) 3 8 (Y1, W1), (Y1, W2) 3 2 Overlap case #1 3 1 (W1 W2) 3.1 i j 4
5 3 Overlap case #2 4 Overlap case #3 5 Overlap case #4 6 Overlap case #5 λ ALL 1 λ i,gf i 1 (Goals For). λ i,ga i 1 (Goals Against). λ i,gf,h λ i,ga,h i 1 λ i,gf,a λ i,ga,a X i i 1 Po(λ) λ. 5
6 7 Overlap case #6 8 Overlap case #7 9 Overlap case # [8] J1 1 M1: X i Po(λ ALL ) p(x) = e λallλx ALL,x = 0,1,. (1) x! P(X i = x,x j = y) = p(x)p(y). (2) M2: X i Po(λ i,gf ) p i (x) = e λi,gf λx i,gf x! 6,x = 0,1,. (3)
7 Observed Poisson 0.3 Frequency Goals 10 Distribution of goals par game P(X i = x,x j = y) = p i (x)p j (y). (4) ( ) λi,gf +λ j,ga M3: i,j X i Po 2 p i,j (x) = e µx µi,j i,j,x = 0,1,. (5) x! µ i,j = λ i,gf +λ j,ga 2 (6) P(X i = x,x j = y) = p i,j (x)p j,i (y). (7) ( ) λi,gf,h +λ j,ga,a M4: i j X i Po 2 p i,j (x) = e µx µi,j i,j,x = 0,1,. (8) x! µ i,j = λ i,gf,h +λ j,ga,a 2 (9) P(X i = x,x j = y) = p i,j (x)p j,i (y). (10) M5: i j i g (λ i,gf,λ j,ga,g) 7
8 (λ i,gf,λ j,ga ) ( ) µ i,j µ(λ i,gf,λ j,ga ) = a 1 λ i,gf +a 2 λ j,ga +a 3 (11) i,j X i Po(µ i,j ) p i,j (x) = e µx µi,j i,j,x = 0,1,. (12) x! P(X i = x,x j = y) = p i,j (x)p j,i (y). (13) λ i,gf, λ i,ga J M5 4 ( ) r 2 = The number of teams reached the postseason Teams M1 M2 M3 M4 M5 case # , 6, 7, , 3, mean M1 M (63) M2 M4 ( ,54.686, ) 8
9 3 Probability of each overlap cases Teams M1 M2 M3 M4 M5 case # x M2 M3 M4 Frequency Points 11 Distribution of points per season M5 4 (Pts) (Mean) (Err) (Std) (Err/Std) µ±1.2σ 2 M1 M [1] 3 4 ( ) 9
10 4 Simulation result with model M5 (total points) Standing Pts Mean Err Std Err/Std * J (Y1 Y3) Y1 ( 12) 4 3 (W1) 4 (W2) W2 1 *3 [5][6] 10
11 12 Basic format of postseason W1 Y2 Y3 W1 1 W2 1 ( 13(a)) W1 Y1 W2 1 Y2 Y3 1 ( 13(b)) 13 One stage winner reaches postseason as repechage 4 2 (W1, W2) 1 1 Y2 W2 Y3 W1 4 Y1 ( 14) 14 Two stage winners reach postseason as repechage 11
12 1 ( 2 ) 2015 J J J 2 1 [1] J League.. Feb referred in 2014/11. [2] Jupiler Pro League. Formule de championnat. (in French), referred in 2014/11. [3] Scottich Professional Football League. The rules of the Scottich Professional Football League therulesofthescottishprofessionalfootballleagueasat11september pdf, Sep referred in 2014/11. [4] ( ). [ ] 2. Oct referred in 2014/11. 12
![[3] Scottich Professional Football League. The rules of the Scottich Professional Football League. http://spfl.co.uk/docs/067 324 therulesofthescottishprofessionalfootballleagueasat11september 2014 1411980004.](/docs-images/51/20155555/images/page_12.jpg "pdf, Sep. 2014. referred in 2014/11. [4] ( ). [ ] 2. http://number.bunshun.jp/articles/-/724962, Oct. 2013. referred in 2014/11. 12")
13 [5] MSN.. Oct refered in 2014/11. [6] J League Oct referred in 2014/11. [7]. 2 ( issue65 ), Nov refered in [8] JohnS. Croucher. Using Statistics to Predict Scores in English Premier League Soccer. In Sergiy Butenko, Jaime Gil-Lafuente, and PanosM. Pardalos, editors, Economics, Management and Optimization in Sports, pages Springer Berlin Heidelberg,
![jp/2013/11/15/post12391/ ( issue65 ), Nov. 2013. refered in 2014.11. [8] JohnS. Croucher.](/docs-images/51/20155555/images/page_13.jpg "Using Statistics to Predict Scores in English Premier League Soccer. In Sergiy Butenko, Jaime Gil-Lafuente, and PanosM.")
22 [21] 2 (NPB) 2007 ( ) 3 ( ) J J ( ) 2 + 2 [5] WBC 2 2015 J1 2 + 3 1 4 2 1 2 + 5 2. 2015 J1 2 + 2015 J1 + [9] 18 2 1 World Baseball Classic
![22 [21] 2 (NPB) 2007 ( ) 3 ( ) J J ( ) 2 + 2 [5] WBC 2 2015 J1 2 + 3 1 4 2 1 2 + 5 2. 2015 J1 2 + 2015 J1 + [9] 18 2 1 World Baseball Classic](/thumbs/39/20144913.jpg "22 [21] 2 (NPB) 2007 ( ) 3 ( ) J J ( ) 2 + 2 [5] WBC 2 2015 J1 2 + 3 1 4 2 1 2 + 5 2. 2015 J1 2 + 2015 J1 + [9] 18 2 1 World Baseball Classic")
Transactions of the Operations Research Society of Japan Vol. 59, 2016, pp. 21 37 c J1 2 + ( 2015 3 14 ; 2015 11 6 ) 2015 J 2 3 4 5 62%, 35%, 3%( 3.4) 5 10 2 1 : 1. J1 2015 2 + [8]( ) 1993 J 2004 2 + 2005
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80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x
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A comparative study of the team strengths calculated by mathematical and statistical methods and points and winning rate of the Tokyo Big6 Baseball Le
Powered by TCPDF (www.tcpdf.org) Title 東京六大学野球リーグ戦において勝敗結果から計算する優勝チームと勝点 勝率との比較研究 Sub Title A comparative study of the team strengths calculated by mathematical and statistical methods and points and winning
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